Just a few days after the launch of the outfit formerly known as Team Sky, following a takeover by Britain's richest man Jim Ratcliffe, Lawless hung on in the fourth and final stage to claim the biggest prize of his career.
Lawless had the backing of four-times Tour de France winner Chris Froome as the peloton headed into Leeds after a tough day of climbing in the Yorkshire Dales.
Olympic champion Greg van Avermaet attacked on the final climb of the day but Lawless would not be dropped and although Van Avermaet won the stage, Lawless took the overall victory with a slender advantage of two seconds.
"Chris really had the legs to go with Greg in the final, which won us the race overall, so really proud of him," Froome told ITV Sport. "For a start for INEOS we could have not asked for much more really."
Froome said he was happy with his own form.
"It's getting better and better," Froome said at the finish. "Still got a long way to go and some hard work ahead of me but that's normal."
Asked where the race win rated in his career, Lawless said: "The biggest. I can't believe it. If someone had told me I'd win this race before it started I'd have called them a liar."
Large crowds again lined the roads for the 182-km ride from Halifax to Leeds -- many of whom will return when the road world championships is held in Yorkshire late this year.
(Reporting by Martyn Herman, editing by Pritha Sarkar)
